1 Introduction
2 Experimental Study
Specimen | Group | f
c
`
(MPa) | ln (mm) | ln/L | hn (mm) | hn/ln | hn/t | Shear reinforcement ratio | |
---|---|---|---|---|---|---|---|---|---|
Vsd % | Vsb % | ||||||||
B0 | G1 | 31.54 | – | 1.00 | – | – | – | – | – |
B2 | 29.82 | 630 | 0.30 | 120 | 0.19 | 0.60 | 0.50 | 0.50 | |
B2 | G2 | 29.82 | 630 | 0.30 | 120 | 0.19 | 0.60 | 0.50 | 0.50 |
B1 | 33.36 | 525 | 0.25 | 120 | 0.23 | 0.60 | 0.50 | 0.50 | |
B3 | 32.18 | 315 | 0.15 | 120 | 0.38 | 0.60 | 0.50 | 0.50 | |
B4 | G3 | 31.72 | 525 | 0.25 | 80 | 0.15 | 0.40 | 0.50 | 0.50 |
B1 | 33.36 | 525 | 0.25 | 120 | 0.23 | 0.60 | 0.50 | 0.50 | |
B5 | 32.26 | 525 | 0.25 | 160 | 0.30 | 0.80 | 0.50 | 0.50 | |
B1 | G4 | 33.36 | 525 | 0.25 | 120 | 0.23 | 0.60 | 0.50 | 0.50 |
B6 | 32.02 | 525 | 0.25 | 120 | 0.23 | 0.60 | 0.50 | 0.80 | |
B7 | 30.67 | 525 | 0.25 | 120 | 0.23 | 0.60 | 0.80 | 0.50 | |
B1 | G5 | 33.36 | 525 | 0.25 | 120 | 0.23 | 0.60 | 0.50 | 0.50 |
B8 | 31.59 | 525 | 0.25 | 120 | 0.23 | 0.60 | 0.80 | 0.80 | |
B9 | 32.48 | 525 | 0.25 | 120 | 0.23 | 0.60 | 0.53* | 0.53* |
2.1 Description of Tested Beam Groups
2.2 Material Properties
2.3 Test Setup and Test Procedure
2.4 Test Results and Discussion
Designation | Group | Cracking properties | Py (kN) | Location of first yield | Pu (kN) | ∆u (mm) | Mode of failure | ||
---|---|---|---|---|---|---|---|---|---|
Pcr (kN) | ∆cr (mm) | Region | |||||||
B0 | G1 | 15.20 | 2.35 | MS | 33.8 | F | 44.40 | 9.91 | SC |
B2 | 3.00 | 0.45 | RE | 11.49 | H | 15.10 | 15.65 | F | |
B2 | G2 | 3.00 | 0.45 | RE | 11.49 | H | 15.10 | 15.65 | F |
B1 | 3.00 | 0.49 | RE | 14.62 | H | 15.70 | 19.50 | SC | |
B3 | 4.30 | 0.48 | RE | 22.30 | H | 24.80 | 15.13 | SC | |
B4 | G3 | 2.60 | 0.30 | RE | 8.48 | H | 10.40 | 18.00 | SC |
B1 | 3.00 | 0.49 | RE | 14.62 | H | 15.70 | 19.50 | SC | |
B5 | 5.50 | 0.91 | RE | 18.38 | H | 21.00 | 28.59 | SC | |
B1 | G4 | 3.00 | 0.49 | RE | 14.62 | H | 15.70 | 19.50 | SC |
B6 | 3.60 | 0.89 | RE | 17.75 | H | 20.50 | 18.99 | SC | |
B7 | 3.20 | 0.24 | RE | 16.72 | H | 19.00 | 13.60 | SC | |
B1 | G5 | 3.00 | 0.49 | RE | 14.62 | H | 15.70 | 19.50 | SC |
B8 | 4.30 | 0.43 | RE | 19.78 | H | 21.00 | 17.85 | F | |
B9 | 5.90 | 1.56 | RE | 16.65 | B | 21.00 | 18.96 | SC |
2.4.1 Crack Pattern and Failure Mode
2.4.1.1 First Group (G1)
2.4.1.2 Second Group (G2)
2.4.1.3 Third Group (G3)
2.4.1.4 Fourth Group (G4)
2.4.1.5 Fifth Group (G5)
2.5 Load–Deflection Response
2.6 Steel Stress–Strain Relationship
3 Numerical Simulations
3.1 Material Properties of Concrete and Steel in the FE Modeling
3.2 Model Set-up
3.3 Sensitivity of Numerical Parameters
3.4 Model Validation
3.4.1 Crack Pattern and Failure Mode
Designation | Group | Cracking properties | Py (kN) | Location of first yield | Pu (kN) | ∆u (mm) | Mode of failure | ||
---|---|---|---|---|---|---|---|---|---|
Pcr (kN) | ∆cr (mm) | Region | |||||||
EXP-B0 | EXP. of G1 | 15.20 | 2.35 | MS | 33.8 | F | 44.40 | 9.91 | SC |
EXP-B2 | 3.00 | 0.45 | RE | 11.49 | H | 15.10 | 15.65 | F | |
FEA-B0 | FEA of G1 | 17.94 | 2.38 | MS | 31.00 | F | 40.40 | 14.75 | SC |
FEA-B2 | 3.81 | 1.88 | RE | 12.82 | H | 16.85 | 18.06 | SC |
3.4.2 Load–deflection response
3.4.3 Load-Steel Strain Relationship
4 Numerical Parametric Study
4.1 Influence of T-Section
FEM | B mm | t mm | As | Cracking properties | Yield properties | Ultimate properties | Failure mode | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Pcr (kN) | ∆cr (mm) | Position | Rcr | P
y
*
(kN) | ∆y (mm) | Ry | Pu (kN) | ∆u (mm) | Ru | |||||
FEA-B2 | – | – | 3.81 | 1.88 | RE | – | 12.82 | 10.02 | – | 16.85 | 18.06 | – | Shear-failure | |
B-300 | 300 | 50 | 8#10 | 27.34 | 1.70 | RE | 7 | 69.00 | 10.38 | 5 | 81.00 | 13.78 | 4.50 | |
B-360 | 360 | 50 | 32.57 | 2.11 | RE | 8 | 74.19 | 10.62 | 6 | 88.00 | 14.55 | 4.88 |
4.2 Influence D-Region Breadth
FEM | b mm | ld mm | As | Cracking properties | Yield properties | Ultimate properties | Failure mode | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Pcr (kN) | ∆cr (mm) | Rcr | P
y
**
(kN) | ∆y (mm) | Ry | Pu (kN) | ∆u (mm) | Ru | |||||
FEA-B2 | – | – | 8#10 | 3.81 | 1.88 | – | 12.82 | 10.02 | – | 16.85 | 18.06 | – | Shear-failure |
B-150 | 150 | 400 | 10.67 | 3.42 | 2.80 | 23.30 | 24.63 | 1.82 | 25 | 31.25 | 1.48 | ||
B-200 | 200 | 400 | 14.67 | 5.43 | 3.85 | 27.86 | 26.94 | 2.17 | 29 | 34.14 | 1.72 | ||
B-150-2100 | 150 | 2100 | 10.59 | 2.82 | 2.77 | 21.56 | 15.31 | 1.68 | 26 | 30.61 | 1.54 |
5 Conclusion
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The location of re-entrant corner affects cracking characteristics, yield load, and ultimate load capacity. Experimental results showed that increasing the beam nib height-to-recess length ratio from 0.19 to 0.23 and 0.38 increases the yield load by 27% and 94% and ultimate load by 4% and 64%, respectively. In addition, the mode of failure changes from pure flexural to compression-shear failure with the decrease in nib length.
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Experimental results showed significant enhancement in the beam ultimate load carrying capacity when using additional closed stirrups along the entire beam span excluding/including nib zone. On the other hand, adding closed stirrups at only the nib zone seemed to have negligible contribution to the load-carrying capacity.
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The use of bent-up bars with ratio of 0.52% at the re-entrant corner resulted in better deflection response and lower damage at re-entrant corner compared to the findings due to the increase in the shear reinforcement ratio along the entire span.
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Good agreement between experimental and FEA results proved the efficiency of the developed numerical model in capturing the nonlinear behavior of the RC beam with unequal depths as depicted from load–deflection response, cracking, failure modes and strain development in reinforcement. Hence, the developed three-dimensional FEA model can be used as a tool for further studies in future.
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Numerical and experimental results confirmed that for RC beams with unequal depths, the sensitivity of the horizontal bar as shear reinforcement seemed to have a significant effect compared to vertical closed stirrups at the re-entrant corner. This may be attributed to the angle of crack growing from re-entrant corner. Also, the position of re-entrant corner can significantly affect the yield load since a higher yield load was reached when using smaller recess length.
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Numerical and experimental findings showed that critical stresses have been generated from re-entrant corner at the initiation of first shear cracking. Also, numerical results agreed with experimental observation in terms of yield location which occurred at the re-entrant corner due to excessive tensile stresses.
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The presence of RC slab, that is cast integrally over the beam with unequal depth, has significant contribution to crack patterns and characteristics (by about 7 to 8 times higher than the non-slab one) as well as yield load values (by about 5 to 6 times higher than the non-slab one) based on the size of the beams considered in this research. Moreover, the presence of the slab changed the mode of failure from the sudden compressive mode (with lower ultimate capacity) to the ductile counterpart (with higher ultimate load).
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Numerical results showed that increasing breadth at D-region (where re-entrant corner exists) by about 50% to 100% resulted in an increase in initial cracking and yield load. Also, the ultimate load capacity has been augmented by about 48% to 72% based on the studies widths in this research. The increase in beam width in only the D-region was found to be more economical and gives better results compared to increasing beam breadth along the whole span length.
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Given the proper development length of the nib tension reinforcement at the re-entrant zone, bond/anchorage failure of such bars was precluded in this study. Design engineer should be attention to bar anchorage length in practice to promote global failure of the beam.